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Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over the years. As a result, almost every chapter in Japanese mathematics textbooks for elementary grades begins with problem solving as a way to introduce students to new concepts and to introduce new procedures. But a large wave of teacher retirement in recent years has left newly hired teachers without the collegial support they need to develop the expertise to teach through problem solving. In order to overcome this challenge, the latest edition of a major mathematics textbook series in Japan includes more resources to help teachers teach through problem solving and to help students learn through problem solving. The book contains more alternative approaches to a problem, provides diagrams meant to help students solve problems independently, and includes pages that teach students how to take notes effectively. By comparing the latest two editions of this textbook series, the author will highlight how the text has increased its support of problem solving, and will relate the changes to recent trends of Japanese mathematics textbook designs.

Several national and international surveys have showed that a very low percentage of Japanese high school students believe mathematics to be useful in daily life. To rectify this issue, problem-based learning (PBL) was introduced into the Japanese mathematics curriculum. However, it is doubtful whether this change will bring about the intended result. Therefore, we propose to integrate entrepreneurship education into PBL in order to develop an attitude of risk taking by using mathematical ways of viewing and thinking. In this study, we developed a framework for gaming instructional material. Moreover, we conducted a trial lesson to evaluate its effects.

The entrance examination for Japan′s university lays a great emphasis on multiple-choice questions, so most of high school students are said to be taught in a way that memorizing the formulae mechanically is the shorter route to high score in test than ever. The best cure for rote memorizing and formulism is to stimulate the intellectual curiosity of undergraduate students newly entering universities. We must make classes more appealing to the freshmen if we are to draw out and cultivate their intellectual curiosity. In Shinshu University, every affiliated faculty assists the Center of Development of Higher Education Programs by sending professors to give the Liberal Arts Lectures from special field of their own. This paper presents the very constructive trial to draw out the intellectual curiosity of the science course students in Shinshu University. Discussions are made on the role of Lecture “Mathematics and Wasan Culture” in stimulating student′s interest. Wasan, the traditional Japanese Mathematics made amazing development as very advanced mathematics equivalent to Western Mathematics. It was widely applied to several technical areas such as map manufacture, astronomical observation and reclamation construction in the era of Edo Period. Especially, an analytical technique in search of a center of gravity of an object is explained by many old Wasan mathematicians. In this lecture, the author used Wasan Problems as the teaching materials. As one of means to improve the analyzing sense of science phenomena, the students learn the old technique used by Wasanka who did not know any formulae of Western Mathematics.

Japanese education has been the subject of considerable research and educational commentary in the United States over the last 20 years. Since the early 1990s, there has been increased interest in Japanese methods for teaching mathematics, and the Third International Mathematics and Science Study has accelerated American interest in Japanese methods. Observational studies, teacher and student surveys, and analyses of classroom videotapes have provided a rich picture of how the Japanese teach the whole class. However, little has been written about how academically low-achieving math students fare in Japanese schools. This article briefly summarizes Japanese methods for teaching mathematics and describes how the educational system addresses academic diversity. It concludes with a description of a method for teaching mathematics that some Japanese mathematics educators feel has promise for students with learning disabilities.

How must n non-overlapping equal circles be packed in a given circle so that the diameter of the circles will be as large as possible? This paper presents an account of this problem and its putative solutions and related configurations in lotus receptacles, classical Japanese mathematics (wasan) and traditional Japanese design. Particular emphasis is placed on the connection between the conjectural solutions of this discrete geometrical problem and the fruit arrangements in the receptacles of lotuses, because in most cases the actual fruit arrangements are identical to the mathematical solutions. As the lotus is an important symbol in Buddhism and lotus decorations are quite common in Japanese Buddhist art, packings of circles in a circle have been represented in Japanese art for centuries.

The Suanxue Qimeng (the Introduction of Mathematics) was written by Zhu Shijie in 1299 during the Yuan dynasty. The book had been lost in the Ming dynasty but was conserved in Korea and reprinted several times as mathematical textbook for the education of mathematical experts of the Korean dynasty. In the last decade of the 16th century a copy of the book was transferred to Japan. In the Edo period in Japan, the book was reprinted several times with annotation. The last chapter of the book explained the procedure of celestial element (tianyuanshu or tengen jutsu), a method for representing a polynomial of one variable with numerical coefficients by a column vector of its coefficients. Having mastered this procedure, Seki Takakazu generalized it in such a way that polynomials of several variables could be handled with.

Connection making is one of the major standards proposed by the National Council of Teachers of Mathematics, however, unlike problem solving, it has no long history of being designated as a goal of mathematics teaching. An examination of classroom observations of mathematics lessons taught in Japan reveal that connection making appears to be an implicit if not explicit standard for Japanese mathematics education. As a perspective from which to re-examine and re-assess our own practice, this paper describes several episodes of connection making as they occurred in Japanese elementary school classrooms. By reflecting upon the methods used in these classrooms, other approaches to connection making are suggested and explored.

We have developed a web-based system of presenting Sangaku. Sangaku is a way of presenting theorems and conjectures in geometry in one sheet of votive picture. Sangaku was used for temples in Japan to exchange geometrical findings, and has been studied as a traditional form of Japanese mathematics called Wasan. We developed a diagrammatic reasoning that directly uses geometric objects as primitives for reasoning, while tools called dynamic geometry software have also been developed. In developing the web-based Sangaku presentation system, we used diagrammatic reasoning which allows users to directly manipulate geometric objects. As a result, geometric findings can be presented not in a static manner of a single picture, but in a dynamic manner of operational geometric objects. Some examples of Sangaku can be seen at: http://www.sys.tutkie.tut.ac.jp/MuJapan.html.

Problems involving tangent circles have been investigated in both the West and the East. In Japan such problems were of special interest in the Wasan period. (" Wasan" refers to Japanese mathematics developed independently of Western science in the 17th-19th centuries.) Wasan researchers often wrote their problems and solutions on a framed board, which was dedicated to a shrine or a temple to express gratitude to the gods. Most such problems were geometric, and the figures were beautifully drawn in color. The board is called a sangaku (votive tablet on mathematics).* It was also a means to publish a discovery or to propose a problem. So Wasan mathematicians thereby left many geometric results (in particular on tangent circles or spheres). We will refer to two such results (for extensive references see [5] or [7]). The author discovered an interesting configuration and consequence of this theorem while considering a problem of the Wasan mathematician Ushijima [8]: "In FIGURE 1, C1, C2, C3, C4 are in circles of the triangles ABD, ADC, AD'C', AB'D' respectively. Given the diameters of C2, C3, C4, find the diameter of C1." The solution essentially states that

Japan has been a member country of IEA since the organization was first established and has participated in all of its mathematics studies: the first in 1964 (FIMS), the second in 1981 (SIMS), the third in 1995 (TIMSS), and most recently in 1999 (TIMSS-R). In addition, Japan has participated in several IEA studies of science education and computer education. Both the results and the methodology of the IEA studies (Robitaille et al., 1993; Robitaille & Garden, 1996) have had a strong impact on Japanese education. In this paper, the impact of the TIMSS results on the Japanese mathematics education are interpreted and discussed. Readers may find it helpful to read more on this topic in the chapter by Miyake and Nagasaki on Japan in The Impact of TIMSS on the Teaching and Learning of Mathematics and Science (Robitaille, Beaton, & Plomp, 2000). LEARNING FROM THE FORMER IEA STUDIES OF MATHEMATICS Mathematics education has a long history in Japan (JSME, 2000). In recent years, lEA’s international mathematics studies have impacted on mathematics education in Japan in a number of ways. Japanese mathematics educators have paid particular attention to students' outcomes in the affective domain and to background information as well as achievement in the cognitive domain. FIMS revealed that higher-achieving Japanese students tended to think of mathematics as stable knowledge to be memorized (NIER, 1967). In response to this, national courses of study developed during the 1970s and 1980s stressed the developmental aspects of mathematics, now more commonly known as “mathematical ways of thinking.” SIMS revealed that Japanese students did not like mathematics and that they thought of mathematics as being irrelevant to society. It further revealed that calculators were not used in mathematics classrooms (NIER, 1981; NIER, 1982; NIER, 1983; NIER, 1991). The national courses of study developed in the 1990s therefore

Wasan, Japanese arithmetic, is an amazing mathematical system. Most people think that there is only one kind of mathematics, just as some philosophies will have us believe that there is only one truth. In fact the Japanese have their own special system which is unique to their culture. We used to believe that modern mathematics was the only type, but we now know that there are different varieties, each with its own value.

In the last few years, numerous articles extolling the virtues of the Japanese educational system have appeared both in academic publications and in the popular press (e.g., Cogan 1984; Morimoto 1982; Shimahara 1985). Although the United States and Japan together lead the industrial world in percentage of young people entering high school (both over 95%), Japanese mean scores on international tests of mathematics and science are consistently higher than those of any other country including the United States (Rohlen 1983). Because of such remarkable results, many Americans are quite interested in knowing more about education in Japan. A six-month-long visit to Indiana University by Toshiaki Yabe, a Japanese elementary school mathematics specialist, provided a unique opportunity for Indiana educators to learn more about Japanese mathematics education and for both sides to benefit from a mutual exchange of ideas. In this article we have collaborated to give a brief overview of Japanese education, followed by some more specific ideas about important considerations in the teaching of mathematics in the elementary grades.